Which of the following statement is correct

Options

A. The centripetal force must be acting on the particle moving in a circular path
B. If no tangential component of thr force is acting on particle moving in circular path, then speed is changing
C. If no tangential component of force is acting on particle moving in a circular path ,the speed of particle changes
D. Both (1) and (3)

Answer

To determine which of the statements regarding circular motion is correct, let's analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** "The centripetal force must be acting on a particle moving in a circular path."

- **Explanation:** This statement is correct. For an object to maintain circular motion, a centripetal force must act towards the center of the circular path. This force is responsible for changing the direction of the object, keeping it in a circular trajectory. The formula for centripetal force is given by \( F_c = \frac{mv^2}{r} \), where \( m \) is the mass, \( v \) is the speed, and \( r \) is the radius of the circular path.

### Step 2: Analyze Statement B
**Statement B:** "If no tangential component of the force is acting on the particle moving in a circular path, then the speed is changing."

- **Explanation:** This statement is false. If there is no tangential component of force acting on the particle, it means there is no force causing a change in the speed of the particle. The speed remains constant as there is no tangential acceleration. The particle can still move in a circular path at a constant speed if only the centripetal force is acting.

### Step 3: Analyze Statement C
**Statement C:** "If no tangential component of force is acting on the particle moving in a circular path, then the velocity of the particle changes."

- **Explanation:** This statement is correct. While the speed (magnitude of velocity) remains constant if there is no tangential force, the direction of the velocity is continuously changing as the particle moves along the circular path. Since velocity is a vector quantity that depends on both magnitude and direction, a change in direction means that the velocity is changing even if the speed remains constant.

### Step 4: Conclusion
Based on the analysis:
- Statement A is correct.
- Statement B is false.
- Statement C is correct.

Thus, the correct answer is that both statements A and C are correct.

### Final Answer:
The correct option is D: Both statements A and C are correct.

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